Continuous convolution semigroups integrating a submultiplicative function

Let be a submultiplicative function on a locally compact group G and let S be a convolution semigroup on G with Lévy measure . It is shown that the measures of S integrate if and only if integrates outside some neighbourhood of the identity of G (Theorem 1). Moreover if (X(t);t0) is the G-valued process with independent increments associated with the semigroup S it is shown that the measures of S integrate if and only if the random variable sup { (X(t)):0t1} is integrable (Theorem 2).     

Automatic differentiation of numerical integration algorithms

Automatic differentiation (AD) is a technique for automatically augmenting computer programs with statements for the computation of derivatives. This article discusses the application of automatic differentiation to numerical integration algorithms for ordinary differential equations (ODEs), in particular, the ramifications of the fact that AD is applied not only to the solution of such an algorithm, but to the solution procedure itself. This subtle issue can lead to surprising results when AD tools are applied to variable-stepsize, variable-order ODE integrators. The computation of the final time step plays a special role in determining the computed derivatives. We investigate these issues using various integrators and suggest constructive approaches for obtaining the desired derivatives.

     

Bonding properties in organolithium aggregates

Results are given of the application of the CNDO/2 method to bonding in alkyllithium aggregates. Calculations relative to monomers and dim ers of methyl-, ethyl-, and vinyllithium, plus methyllithium tetramer are described.     

A sequential auction involving asymmetrically-informed bidders

An example is given of a sequential auction in which, at equilibrium, the expected profit of an informed bidder may be strictly less than the expected profit of an uninformed bidder. This phenomenon is interpreted in terms of the internal game between a player's “types” which arises in a setting of incomplete information.     

Über einen neuen Existenzsatz für Flächen vorgeschriebener mittlerer Krümmung

Ohne Zusammenfassung     

Betrachtungen zu einer vereinheitlichten Kerntheorie

In the beginning it is shortly reviewed how one can obtain in the frame of the Rayleigh-Schrödinger variational principle a unified structure and reaction theory which includes any kind of bombarding particles and reaction fragments. Then methods are discussed which allow to simplify the practical reaction calculations. Special emphasis is given to the question how in a natural way one can connect shellmodel- and cluster-calculations. Finally it is shortly mentioned how one can apply similar considerations to the atomic- and molecular-reactions.     

Steifigkeitsmatrizen dünnwandiger Stäbe und Stabsysteme

Übersicht Die Steifigkeitsmatrizen dünnwandiger Stäbe werden nach der vereinfachten Theorie im Hauptsystem abgeleitet und auf exzentrische Knotenpunkte transformiert. Die Schubdeformation der Stabmittelfläche wird näherungsweise erfaßt. Neben der wölbfreien und wölbstarren Aussteifung wird die wölbelastische Aussteifung berücksichtigt.

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Summary The stiffness matrices of thin-walled bars are determined and transformed to excentric nodal points starting from the simplified theory. The shear strain of the middle plane of the bar is approximately included. The warping elasticity of the stiffener is considered including free warping and completely suppressed warping.

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Bericht des Instituts für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen der Universität Stuttgart (ISD), Direktor: Professor Dr. Dr. h. c. J. H. Argyris.